An electron is moving in one dimension in an infinitely high potential box of width 1 Å. What is the energy of the electron?

A) 37.6 eV
B) 150.4 eV
C) 13.6 eV
D) 40.8 eV

Question

High School

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Answer :

soniaverma40 soniaverma40 · Answer 1 · 2023-09-21T05:44:42-04:00

The energy of the electron moving in a one-dimensional infinitely high potential box of width 1 Å is approximately 37.6 eV.

The energy of an electron moving in a one-dimensional infinitely high potential box can be determined using the formula:

E = (n2h2) / (8mL2)

Where:

E is the energy of the electron
n is the quantum number representing the state of the electron (in this case, it is the ground state, so n = 1)
h is the Planck's constant (6.62607015 × 10-34 Js)
m is the mass of the electron (9.10938356 × 10-31 kg)
L is the width of the box (in this case, 1 Å = 1 × 10-10 m)

Substituting the values into the formula, we have:

E = (12 × 6.62607015 × 10-34 Js2) / (8 × 9.10938356 × 10-31 kg × (1 × 10-10 m)2)

After calculating, the energy of the electron is approximately 37.6 eV.